SOLUTION: find the area of a regular nonagon whose sides measure 3 millimeter. Determine the number of distinct diagonals that can be drawn from each vertex and the sum of its interior angle

Algebra ->  Polygons -> SOLUTION: find the area of a regular nonagon whose sides measure 3 millimeter. Determine the number of distinct diagonals that can be drawn from each vertex and the sum of its interior angle      Log On


   

Question 1119266: find the area of a regular nonagon whose sides measure 3 millimeter. Determine the number of distinct diagonals that can be drawn from each vertex and the sum of its interior angle
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
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find the area of a regular nonagon whose sides measure 3 millimeter.
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central angle of the nonagon, 360%2F9=40 degrees

The nonagon's side for one of these sections forms a base of a triangle. From center of the nonagon to midpoint of the base, is "height" of triangle. This height: %283%2F2%29%2Fh=tan%2820%29 for height h;
3%2F%282h%29=tan%2820%29

2h%2F3=1%2Ftan%2820%29

h=%283%2F2%29%2Ftan%2820%29

h=3%2F%282%2Atan%2820%29%29

Area of one of these triangles: %281%2F2%29%2A3%2Ah
%281%2F2%293%2A%283%2F%282%2Atan%2820%29%29%29
9%2F%284%2Atan%2820%29%29

The nonagon contains nine of these triangles:
Area of the entire nonagon:
highlight%2881%2F%284%2Atan%2820%29%29%29mm%5E2